Descriptive Statistics

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Descriptive Statistics

• 2.5 Describing Qualitative Data
• 2.6 Using Scatter Plots to Study the Relationship
  Between Variables

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2.5 Describing Qualitative Data

• Values of qualitative variables are already
  divided into specific categories
• A frequency distribution is a table with two
  columns a list of categories and the number or
  percentage of values in each of the listed
  categories

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Describing Qualitative Data

• A bar chart is a graphical depiction of a
  qualitative frequency distribution
• Each separate bar represents a category
• Bar heights represent the number or percentage of
  observations in each category
• Unlike histograms the bars are separated by spaces

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Bar Chart
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Side by Side Comparison with Bar Chart
Percentage of Automobiles Sold by
Manufacturer, 1970 versus 1997
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Side by Side Comparison with Bar Chart
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Describing Qualitative Data with Pie Charts

• A pie chart is an alternative way to graphically
  depict a qualitative frequency distribution
• Best for representing each category as a
  percentage of the all observed categories
• Each slice represents a category
• The larger the category percentage the larger the
  slice angle, q

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Pie Chart Example
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Pie Chart
Percentage of Automobiles Sold by
Manufacturer,1997
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Population and Sample Proportions in Qualitative
Frequency Distributions Focus on One Particular
Category of Interest
Population X1, X2, , XN
p
Population Proportion
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Example Sample Proportion
Example 2.16 Marketing Ethics Case 117 out of
205 marketing researchers disapproved of action
taken in a hypothetical scenario
X 117, number of researchers who disapprove n
205, number of researchers surveyed Sample
Proportion
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Pareto Charts

• The Pareto principle often applies to defects in
  a manufacturing or service process
• Only a few defect types account for most of a
  products quality defects
• Quality control objective divide defect types
  into two categories of the vital few and the
  trivial many
• Depict with a modified bar chart

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Pareto Charts

• Construct a bar chart with defect types as the
  categories
• Arrange the categories in descending order of
  frequency or percentage
• Keep track of the cumulative frequency of defect
  types to separate the vital few from the
  trivial many
• Typically vital few account for 75-80

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Pareto Chart
Pareto Chart of Labeling Defects
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Describing Relationship Between Two Variables

• Variable of Interest dependent or response
  variable (quantitative), denoted by Y (e.g.
  salary)
• Variables related to Y-variable independent or
  explanatory variable. Denoted by X can be
  quantitative or categorical (e.g. years of
  experience, gender)
• Describe relationship with scatter-plot
  Y-vertical axis, X horizontal axis

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2.6 Scatter Plots
Restaurant Ratings Mean Preference vs. Mean Taste
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Scatter Plot Characteristics

• Form Overall pattern of scatter. Can be linear
  or curved
• Direction Positive pattern from S.W. to N.E,
  Negative pattern from N.W. to S.E.
• Strength The tighter the scatter pattern the
  stronger the relationship. A shot-gun blast
  indicates no relationship exists between Y and X

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The Correlation Coefficient
The simple correlation coefficient measures the
strength of the linear relationship between y and
x and is denoted by r.
r is a number between 1 and -1 r 1 if
scatterplot forms an exact straight line r 0
for a shot-gun blast pattern
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Different Values of the Correlation Coefficient
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Assessing Linear Relationships with r
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Scatter Plot with Categorical X-variable
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Not all relationships are linear